Find the minimum value of f(x)=2x^{3}+3 in the interval [-2,2]. The

Joyce Smith

Joyce Smith

Answered question

2021-12-11

Find the minimum value of f(x)=2x3+3 in the interval [-2,2].
The absolute minimum value is 5 at x=1.
The absolute minimum value is 3 at x=0.
The absolute minimum value is -13 at x=-2.
The absolute minimum value is 19 at x=2.

Answer & Explanation

Shannon Hodgkinson

Shannon Hodgkinson

Beginner2021-12-12Added 34 answers

Step 1
We first find the critical point by solving f'(x)=0
f(x)=2x3+3
f(x)=6x2
0=6x2
x2=0
x=0
Step 2
Then we check the values of f(x) at the critical point and the endpoints
f(x)=2x3+3
At x=-2, f(-2)=-13
At x=0, f(0)=3
At x=2, f(2)=19
So the minimum value is -13.
Answer: The absolute minimum value is -13 at x=-2

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